Taking the Risk out of Systemic Risk Measurement I by Levent Guntay and Paul Kupiec1 Draft: January 6, 2014 ABSTRACT an Emergi
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Taking the risk out of systemic risk measurement I by Levent Guntay and Paul Kupiec1 Draft: January 6, 2014 ABSTRACT An emerging literature proposes using conditional value at risk (CoVaR) and marginal expected shortfall (MES) to measure financial institution systemic risk. We identify two weaknesses in this literature: (1) it lacks formal statistical hypothesis tests; and, (2) it confounds systemic and systematic risk. We address these weaknesses by introducing a null hypothesis that stock returns are normally distributed. This allows us to separate systemic from systematic risk and construct hypothesis tests for the presence of systemic risk. We calculate the sampling distribution of these new test statistics and apply our tests to daily stock returns data over the period 2006-2007. The null hypothesis is rejected in many instances, consistent with tail dependence and systemic risk but the CoVaR and MES tests often disagree about which firms are potentially “systemic.” The highly restrictive nature of the null hypothesis and the wide range of firms identified as systemic makes us reluctant to interpret rejections as clear evidence of systemic risk. The introduction of hypothesis testing is our primary contribution, and the results highlight the importance of generalizing the approach to less restrictive stock return processes and to other systemic risk measures derived from return data. Key Words: systemic risk, conditional value at risk, CoVaR, marginal expected shortfall, MES, systemically important financial institutions, SIFIs 1 The authors are, respectively, Senior Financial Economist, Federal Deposit Insurance Corporation and Resident Scholar, The American Enterprise Institute. The views in this paper are those of the authors alone. They do not represent the official views of the American Enterprise Institute or the Federal Deposit Insurance Corporation. Emails: [email protected] (corresponding author), [email protected]. Taking the risk out of systematic risk measurement I I. Introduction A number of recent papers have used specific measures of stock return tail dependence as indicators of the “systemic risk” potential associated with individual large complex financial institutions.2 This literature suggests that specific stock return tail dependence measures can be used as a basis to tax large complex financial institutions and penalize them for the systemic risk that they create [1,2], or alternatively, to indirectly tax these institutions by requiring enhanced regulatory capital and liquidity requirements that are calibrated using these tail dependence measures [3]. In this paper, we focus on two systemic risk measures that have been proposed in the literature: conditional value at risk (CoVaR) and marginal expected shortfall (MES). Both measure tail dependence in the stock returns of individual financial institutions and equate the magnitude of tail dependence estimates as a measure of systemic risk created by the institution in question. The basic idea in the systemic risk literature is that, should a systemically important financial institution suffer a large loss and become distressed, it will shift the lower tail of the stock return distributions of other firms in the economy. The shift happens because the institution’s distress spreads throughout the financial sector and chokes off credit intermediation to the real economy. The claim is that the systemic risk potential of an institution can be measured using either CoVaR or MES applied to financial institution stock return data. CoVaR and MES differ on the exact set of conditioning events but each borrows a popular measurement technique from the risk management literature and applies it to conditional returns distributions as means for identifying and measuring a financial institution’s systemic risk. The CoVaR measure of systemic risk proposed in the literature is the difference between two 99 percent VaR3 measures applied to the conditional return distribution of a portfolio of financial institutions: (1) the 99 percent CoVaR conditional on the single financial institution in question experiencing a return equal to its 1 percent quantile; and, (2) the 99 percent CoVaR conditional on the same individual institution experiencing a median return.4 The idea is that, should there be systemic risk potential, a near catastrophic loss by the financial institution in question will left-shift the 1 percent quantile of the conditional return distribution of a portfolio of financial firms. CoVaR is typically estimated using 2 These papers include [1], [2], [3], and [6]. See [5] for a recent survey of this literature and [7] or [4] for a critical assessment. 3 In this literature, a 99 percent VaR measure is taken to be identical to the 1 percent quantile of the underlying return distribution. 4 CoVaR is very similar to the value at risk stress testing methodology developed in [8]. 2 quantile regression on the grounds that such estimates are non-parametric and free from biases that may be introduced by inappropriately restrictive distributional assumptions. Expected Systemic Shortfall (SES) and the Systemic Risk Index (SRISK) are transformations of the MES. MES is the expected shortfall calculated from a conditional return distribution for an individual financial institution. The institution’s return distribution is conditioned on a large negative market return. SES and SRISK measures transform MES so that it approximates the extra capital the financial institution may need to survive a virtual market meltdown. SES and SRISK measures are based on MES and measures of the financial institution’s capital and leverage. The primary input is the financial institution’s MES which is typically estimated as the institution’s sample expected stock return value on days when the market return realization is in its 5 percent lower tail. This measure is also non-parametric in the sense that the estimator requires no maintained hypothesis about the probability density that generates stock returns. The existing literature asserts that when large complex financial institutions exhibit large CoVaR or MES estimates it is evidence that these institution have the potential to create significant systemic risk. Existing studies demonstrate the “power” of these systemic risk measures by showing that virtually all of the large financial institutions that required government assistance during the recent financial crisis (or failed) exhibited large CoVaR or SES measures immediately prior to the crisis. Moreover, the nonparametric nature of the methods that have been used to estimate CoVaR and the MES has been portrayed as positive attribute because they avoid the introduction of biases that may accompany inappropriate parametric distributional assumptions. In our view, there are two glaring weaknesses in the existing CoVaR and MES systemic risk literature. One weakness is that the literature does not offer formal statistical hypothesis tests to identify systemic risk. A second weakness is that the CoVaR and MES measures are contaminated by systematic risk.5 Firms that have large systematic risk will have a tendency to produce large (negative) CoVaR and MES statistics even when there is no evidence of systemic risk in their returns. Existing CoVaR and MES studies have thus far avoided the use of formal hypothesis tests. They do not specify a model for the null hypothesis of “no systemic risk” that is tested and rejected in favor of the alternative hypothesis that the institution is a source of systemic risk. Instead they argue it is not mere coincidence that the large complex institutions that failed or received government aid also had large MES or CoVaR measures prior to the onset of the crisis. For a literature that is based on relatively complex 5 See, for example [7] or [4]. 3 statistical arguments, it is surprising that it chooses to eschew basic principles of classical statistical inference. The nonparametric nature of the recommended estimators for the CoVaR and MES metrics has helped to obscure their underlying portmanteau nature. Adopting a classical view of statistical inference, under the null hypothesis of no systemic risk, the sample values of the CoVaR and MES statistics can only be generated by systematic (market) and idiosyncratic risks. Under the alternative hypothesis of systemic risk, the CoVaR and MES sample statistics will still be generated by systematic and idiosyncratic risk (perhaps largely so), but there will be an additional element of “systemic risk” in the returns data as well. The null hypothesis of no systemic risk should be rejected when the sample includes ample evidence that there is a large systemic risk component present in the sample return data. The lack of a well-defined null hypothesis in existing CoVaR and MES studies precludes the possibility of constructing a formal test statistic. Such a statistic is needed to identify when a sample of stock returns is sufficiently different from the null hypothesis so that it is appropriate to reject the null hypothesis of no systemic risk. In this paper, we take a first step toward removing these shortcomings in the existing systemic risk literature. We consider the parametric formulation of CoVaR and MES measures under the null hypothesis that stock returns are a multivariate Gaussian process. The Gaussian return distribution is symmetric and exhibits tail independence meaning that, in the bivariate case, the probability of observing an extreme return in one dimension is not affected by an extreme return realization